An expedient method of measuring the angular rate of rotation about a given coordinate axis involves dithering an accelerometer so that it moves back and forth along an axis normal to the accelerometer's sensitive axis, and normal to the axis about which rotation is to be measured. For example, if the accelerometer is mounted on a body with its sensitive axis aligned with the Z axis of a set of X, Y, and Z orthogonal coordinate reference axes, the accelerometer will sense a Coriolis rate acceleration if the body rotates about the X axis while the accelerometer is driven to vibrate or dither back and forth along the Y axis, with a periodic motion. The output of the accelerometer includes a component representing acceleration of the body along the Z axis and a periodic component that represents rotation of the body about the X axis. The accelerometer output can be processed, along with the outputs of accelerometers that have their sensitive axes aligned with the X and Y axes and that are moved along the Z and X axes, respectively, to yield linear acceleration and angular rate about all three axes, X, Y and Z. Such signal processing is described in U.S. Pat. Nos. 4,445,376, and 4,590,801.
In U.S. Pat. No. 4,510,802, a rotational rate sensor is disclosed that implements the above rate sensing technique. As described in this patent, two accelerometers are mounted in a parallelogram structure with their sensitive axes parallel or antiparallel. The two accelerometers are vibrated back and forth in a direction substantially normal to their sensitive axes by an electromagnetic coil that is energized with a periodically varying current. The varying magnetic attractive force of the coil causes the parallelogram structure to vibrate or dither at a fixed frequency, typically around 100 Hz. A signal processor connected to the pair of accelerometers combines their output signals, deriving both a rate signal and a linear acceleration signal. Three such pairs of accelerometers can provide rate and linear acceleration for each of the orthogonal X, Y and Z axes.
Although analog accelerometers may be used in the above-described Coriolis rate sensor, it is preferable to use a device, such as a vibrating beam accelerometer, which produces an output signal having a frequency that varies with the sensed acceleration to facilitate digital processing of the output signal. In a vibrating beam accelerometer, a proof mass is supported by a flexure hinge and a vibrating beam force sensing element. A drive circuit causes the force sensing element to vibrate at its resonant frequency, and that frequency varies with the force (or acceleration) acting on the force sensing element. As the force changes due to acceleration, the resonant frequency is modulated higher or lower.
A synchronous FM digital detector is disclosed in U.S. patent application, Ser. No. 789,657, for demodulating the output signals from a pair of vibrating beam accelerometers comprising a rate sensor. The detector derives the rate and linear acceleration data from the modulated resonant frequencies of the accelerometers, and includes processing means for determining for each output signal, the difference between the phase change of the output signal during a first and a second time period, defined by a reference signal. The periodic motion of the pair of accelerometers is controlled by a movement signal, sin .omega.t. The first and second time periods together span one or more complete periods of the movement signal, during which, the Coriolis components of acceleration have opposite polarity. The processing means are operative to determine from the phase values, the angular rate of rotation of the body to which the pair of accelerometers are fixed.
Several simplifying assumptions are made in calculating the angular rate of rotation according to the above method. For example, it is assumed that both the linear acceleration and angular rate of rotation are constant over the complete period of the movement signal, i.e., over one complete dither cycle. Third and higher order cross-coupling terms comprising error components of the accelerometer output signals are ignored. The assumptions used in this prior art synchronous demodulator may introduce substantial and unacceptable "random walk" errors if applied to a body subject to a severe dynamic environment, i.e., rapid changes of velocity, direction and angular rotation. Since the prior art method uses a full wave demodulation technique, it severely restricts the rate at which angular rate and linear acceleration data may be developed for a moving body. This restriction on the data rate occurs because the dither frequency limits the time resolution of incremental changes in velocity and angular position. For this reason, it would obviously be desirable to use a higher frequency movement signal to vibrate the accelerometers back and forth at a faster rate; however, it is impractical to dither the mass of a parallelogram structure at a frequency much higher than about 100 Hz. For a fast-moving, dynamically energetic body, such as a missile, the 0.01 second data resolution period provided by the prior art method is unacceptably long.
In consideration of these problems, it is an object of the present invention to substantially increase the rate at which linear acceleration and angular rate of rotation data are determined. A further object of this invention is to correct the data thus produced for errors previously ignored in the prior art method. These and other objects and advantages of the invention will be apparent from the attached drawings and the description of the preferred embodiments that follows.